Uniform Exponential Stability Approximation For Two Kinds Of Hyperbolic Partial Differential Systems

The mathematical model of partial differential equation can simulate many engineering and technical problems.As a basic partial differential equation,the study of numerical approximation of hyperbolic partial differential equation has important theoretical value.In this paper,we mainly study the approximation of spatial semi-discrete uniform exponential stability for two kinds of hyperbolic partial differential systems.Firstly,the problem of spatially semi-discrete uniform exponential stability approximation for a special class of one-dimensional wave systems is studied.The order of the onedimensional wave system is reduced by introducing intermediate variables,and the original system is transformed into an equivalent continuous system.The exponential stability of the continuous equivalent system is proved by using the Lyapunov function method.A spatial semi-discrete finite difference scheme is constructed for equivalent systems,and the discrete auxiliary function is introduced to study the uniform exponential stability approximation of semi-discrete systems.Numerical experiments verify the uniform exponential decay of the system energy.Secondly,the problem of spatially semi-discrete uniform exponential stability approximation for thermal-convective coupled systems is studied.By introducing intermediate variables and reducing the order of the system based on the reduced order method,the original system is transformed into an equivalent continuous system,and the exponential stability of the equivalent system is proved.For the equivalent system,the spatial semi-discrete finite difference scheme on the equidistant grid is constructed,and the uniform exponential stability of the semi-discrete system is proved by the discrete multiplier method.Numerical experiments verify the exponential stability of discrete systems.